Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
2648 conjugacy classes of subgroups; only the 483 normal subgroups are shown.
This group has 2648 conjugacy classes of subgroups — too many to draw. Only its 483 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×C5⋊D5 |
| commutator, cosocle | C22×C52 | C24 |
| Frattini | C22 | C23×C5⋊D5 |
| Fitting | C25×C52 | C2 |
| socle | C23×C52 | C23 |
| hypercenter | C25 | C5⋊D5 |
| hypocenter | C52 | C2×#120 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C25 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×C52 | C2 | semidirect |
| 2. C22×C22⋊(C5⋊D5) | C2 | semidirect |
| 3. #11717273 | C2 | direct (N × H) |
| 4. C2×C22⋊#1039 | C2 | semidirect |
| 7. C24×C52 | C22 | semidirect |
| 8. C23×C5⋊D5 | C22 | semidirect |
| 10. C2×C22⋊(C5⋊D5) | C22 | semidirect |
| 11. C22×#1039 | C22 | semidirect |
| 12. C22⋊#1039 | C22 | semidirect |
| 17. C23×C52 | D4 | semidirect |
| 21. C22×C5⋊D5 | C23 | semidirect |
| 24. C2×#1039 | C23 | semidirect |
| 25. C25×C5 | D5 | semidirect |
| 33. C22×C52 | C2×D4 | semidirect |
| 40. C24×C5 | C2×D5 | semidirect |
| 48. C2×C52 | #120 | semidirect |
| 54. C23×C5 | C22⋊D5 | semidirect |
| 62. C25 | C5⋊D5 | semidirect |
| 66. C52 | C2×#120 | semidirect |
| 71. C22×C5 | C2×C22⋊D5 | semidirect |
| 79. C24 | C2×C5⋊D5 | semidirect |
| 85. C2×C5 | #4099 | semidirect |
| 93. C23 | C22⋊(C5⋊D5) | semidirect |
| 99. C5 | C2×#4099 | semidirect |
| 106. C22 | C2×C22⋊(C5⋊D5) | semidirect |
| 111. C2 | #11717273 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C52 | 2 |
| C22×C22⋊(C5⋊D5) | 2 |
| #11717273 | 2 |
| C2×C22⋊#1039 | 2 |
| C2×#4099 | 5 |